1. Field of the Invention
The present invention relates to the quantitative analysis of samples such as grains, fruit, chemicals, and other materials by measuring the absorptivity of the samples to electromagnetic radiation such as near infrared radiation.
2. Description of the Prior Art
As exemplified in U.S. Pat. Nos. 3,776,642, 3,828,173, 3,861,788 and 4,286,327, the prior art contains a number of apparatus and processes for analyzing samples such as grains for moisture, protein and oil content utilizing near infrared quantitative analysis wherein readings of the absorptivity of the samples to near infrared radiation at several selected narrow bandwidth wavelengths are obtained and processed by a computer to determine the quantity of one or more constituents of the samples. These readings can be obtained by various arrangements of an infrared source or sources such as infrared emitting diodes (IREDs) or lamps, filters, and an infrared detector or detectors such as silicon photocells or lead sulphide photodetectors. The filters may be stationary in branch optical paths from respective IREDs or to respective detectors or on a tilting paddle wheel or a rotating disc for passing through a single optical path between a source and a detector. Each detected signal is generally amplified logarithmically or converted to a logarithmic scale in a computer to obtain an optical data reading of absorptivity OD which is equal to log 1/T where T is the percent of infrared energy transmitted at the selected wavelength or which is equal to log 1/R where R is the percent of infrared energy reflected at the selected wavelength. Alternatively, the absorptivity or optical data values OD need not be logarithmic and can be equal to 1/T or 1/R or some other function of transmissivity or reflectivity. The optical data readings are processed in a computer to obtain the percentage (%) of each constituent in accordance with an algorithm or formula such as one of the following well known formulas: ##EQU1##
The formula (1) is a multiple linear equation wherein the constants K.sub.o -K.sub.n are determined by multiple regression techniques, i.e., optical readings are obtained from the sources, filters and detectors of the instrument being constructed for a representative number of grain samples which have been accurately analyzed by laboratory test equipment, and the optical readings and previously measured percentages are utilized to calculate sets of K.sub.o -K.sub.n values for the respective moisture, oil and protein content using a conventional regression algorithm in a digital computer. These sets of K.sub.o -K.sub.n values are then programmed into the analyzing instrument being constructed so that the instrument can directly compute the constituent percentages (moisture, oil, protein, etc.) from optical data readings.
Formula (2) is similar to the Formula (1) except that the first derivatives of the optical data readings OD.sub.1 -OD.sub.n are utilized. In the computer, the first derivatives are approximated by the difference between two adjacent optical readings such as in the formula: EQU dOD.sub.1 =OD.sub.1 -OD.sub.2 ( 6)
Formula (2) has the advantage that accurate percentages can be constituted utilizing less optical data terms and the derivative terms provide correction for voltage drifts in instrument readings.
Formula (3) computes a normalized first derivative by dividing the derivative of a reading at one selected point 1 by derivatives of readings at a second point C; the first and second point being selected to produce the numerator and denominator needed to calculate the desired percentage over a broad range of constituent values. These points further are selected to compensate for light-scattering and mutual interferences. Sets of values K.sub.o and K.sub.1 are determined, like the values K.sub.o -K.sub.n in formulas (1) and (2), by multiple regression techniques. Formula (3) may have a single first derivative term or may have several single derivative terms.
Formulas (4) and (5) are similar to Formulas (2) and (3) except that second derivatives of the optical readings are utilized; the second derivatives are derived by approximation utilizing the formula: EQU d.sup.2 OD.sub.1 =OD.sub.2 +OD.sub.3 -2OD.sub.1 ( 7)
wherein OD.sub.2 and OD.sub.3 are adjacent optical readings taken at wavelengths slightly lower and slightly higher than OD.sub.1.
The multiple linear equation (4) utilizing second derivatives and the equation (5) with normalized second derivative terms are more complex but provide versatile approaches enabling accurate results from fewer readings as well as improved compensation for light scattering, and mutual interferences.
In prior U.S. patent application Ser. No. 355,325, filed Mar. 8, 1982, there is described the use of a formula of the type: EQU %=K.sub.o +K.sub.1 OD.sub.1 +--+K.sub.n OD.sub.n +K.sub.G T.sub.G +K.sub.A T.sub.A ( 8)
wherein:
T.sub.G =Grain or sample Temperature PA1 T.sub.A =Ambient Temperature PA1 K.sub.G and K.sub.A are constants which are determined along with K.sub.o -K.sub.n by multiple regression techniques including readings made at different temperatures. The inclusion of the terms K.sub.G T.sub.G and K.sub.A K.sub.A compensates for changes in optical data readings due to different temperatures of the grain or sample, and of the testing instrument.
Generally the desired wavelengths used in the above algorithms for analyzing various grains and other materials are well known in the art and are found in various publications. Analytical and empirical techniques are often used to optimize the selected wavelengths.
In the manufacture of infrared quantitative analytical instruments, the determination of the constants K by multiple regression techniques generally requires about ten samples for each constant to be determined. For the formula (8) where about twelve optical data terms are utilized, about one hundred fifty samples are required to calibrate the instruments. Utilization of less samples results in K values which produce inaccurate results in measuring samples which vary from the samples used in calibration. The maintenance and analytical laboratory procedures for the large number of different samples add substantially to the costs of manufacturing instruments. Thus utilization of algorithms with fewer terms, such as algorithm (5), is desirable to lower costs of maintaining and analyzing calibration samples.
The algorithms employing derivatives, and especially second derivatives, are also desirable since they produce superior results from samples which vary from the calibration samples. In use of algorithm (1) and, to a somewhat lesser degree, algorithms (2) and (3), inaccurate constituent percentages can be produced where the sample being analyzed varies from the samples used in calibration. Particularly inaccurate constituent percentages can be produced where the calibration samples are not sufficiently varied in constituents to closely cover the range of constituents in which the sample being analyzed is found. The algorithms with derivative terms, and especially second derivative terms, are much more accurate when the sample being analyzed varies from the samples used in calibration.
One problem in the manufacture of relatively low cost commercial instruments concerns the inability to obtain readings at precise wavelengths. Generally, the instruments must employ narrow band pass optical filters in order to obtain readings at the desired wavelengths. Unfortunately, the reasonably priced, commercially available narrow band pass filters have actual center wavelength responses which vary up to about .+-.2nm together with a similar half power band width tolerance from their nominal responses. The algorithms (2) and (3) employing fewer terms with first derivatives are more wavelength sensitive than the multiple linear equation (1) employing twelve or more terms of basic optical data readings, and the algorithms (4) and (5) employing second derivatives are even more wavelength sensitive such that the normal tolerance or variations in the available filters hinders the employment of single or low term derivative formulas in relatively low cost instruments. Expensive laboratory instrumentation such as a scanning monochrometer, can be utilized to obtain accurate wavelength information suitable for use by algorithms employing first and second derivatives. Besides being relatively expensive, the scanning monochrometers are relatively more prone to mechanical problems and failure.
Another approach to obtain accurate wavelength readings is to adjust the tilt of each narrow band pass filter in construction of the instrument. Tilting of a band pass filter causes slight shifts in the center wavelength response of the filter, thus allowing the filter to be adjusted to an accurate wavelength. The relationship between the tilt angle and center wavelength response is nonlinear, and accurate adjustment of the tilt angle to accurately tune each filter is difficult to perform.
In the "tilting filter paddle wheel" approach, a large number of readings can be made at closely spaced wavelengths. In addition to the difficulties from the nonlinearity of the tilt angles and wavelengths responses, this approach also requires accurate encoders and other precision optical and mechanical devices along with time consuming manufacturing procedures which make the cost of such instruments relatively higher.
Still another approach to overcoming the wavelength variation of filters is to sort individual filters so as to utilize only filters with the desired accurate wavelength response; however, the yield of acceptable filters is too small to render this approach practical since most of the filters would be unusable resulting in increased costs.